For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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1answer
31 views

Sphere - Sphere intersection cone angle

Consider the formation of a lens by intersection of two spheres. How can I calculate the cone angles formed for each spheres formed by the line connecting the centers of the spheres and the line ...
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0answers
17 views

(Kiselev) Construction of an arc of a circle

Using only compass, construct a 1 degree arc on a circle, if a 19 degree arc of this circle is given. The first thing that is stumping me is if we can use a straight edge? In any case, I can think of ...
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0answers
21 views

connections between polar set, polar cone?

Given a set $S$, its polar cone http://en.wikipedia.org/wiki/Dual_cone_and_polar_cone and its polar set http://en.wikipedia.org/wiki/Polar_set are defined. Could some please tell me the ...
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1answer
27 views

Calculating the volume of an oblique ellipse cone

I am trying to calculate the volume of an oblique cone that is an ellipse (rather than a circular cone). I have the following measurements Perimiter of the Ellipse (in cm) Slant Height of longer ...
3
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0answers
24 views

How to calculate a reduced volume?

Let's say we have an irregular 3D shape with volume=V ( we know V but we don't know its equation= F). Now I want to calculate another 3D shape which is exactly the same shape but one size smaller, ...
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1answer
23 views

Identifying compositions of reflections, and rotations in a hexagon

Let $ABCDEF$ be a regular hexagon that is oriented clockwise (so that a rotation from $A$ to $B$ to $C$ to $D$ to $E$ to $F$ is clockwise). i) Identify $R_{D,120} \circ R_{A,60}$ which are two ...
3
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2answers
64 views

Distance between two rectangulars

I have faced a problem, that I need to calculate a shortest distance between two rectangulars, which are on a different angles. Known parameters: length, width, angle and coordinate of center ...
3
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0answers
14 views

Intersection of the composition of two glide reflections

i am taking a geometry course and we are learning about isometries. I am having a hard time with glide reflections and this problem is giving me some issue, mainly because my professor usually tells ...
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3answers
61 views

How to find the area of the following triangle

I am stuck on the following problem: Let ABC be an isosceles triangle having two equal sides of length $20$ cm. and the angle between the two equal sides is $45^{\circ}$. Then I have to find ...
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1answer
11 views

Find the number of triangles formed by 2 parallel points and a non-collinear point.

There a 11 points on a plane with 5 lying on one straight line and another 5 lying on a second straight line which is parallel to the first line. The remaining point is not collinear with any two of ...
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0answers
16 views

Show if a point belongs to the area of a complex polygon

I would like to know if there is a way to know if a point belongs to the area of any polygon just by knowing the coordiantes of all the points making the boundary of the polygon , given thaht where I ...
4
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1answer
52 views

Can some one help me parametrize $\frac{x^4}{a^4}+\frac{y^4}{b^4}+\frac{z^4}{c^4}=1$

Given a surface $$\frac{x^4}{a^4}+\frac{y^4}{b^4}+\frac{z^4}{c^4}=1$$how can I parametrize the surface using $X(u,v).$ I tried to use $$x=a\sqrt{\cos(\theta)\sin(\phi)}$$ ...
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0answers
25 views

3D vector perpendicular calculation

Three points $A(6,7,-6)$,$ B(0,0,0)$ and $C(2,6,9)$ are given which are the vertices of a cubes. Find the coordinates of another vertex not on the $ABCD$ plane. I found the answer by finding the ...
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2answers
29 views

Three circles, 5 points of intersection, prove that two circles are tangent

There are 3 circles and 5 points of intersection (point of intersection is a point where at least 2 circles meet). Prove that two circles are tangent (it means that they intersect in a single point)
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0answers
51 views

Expected distance of a moving object [closed]

I want to find the expected distance of a moving object from the center of a circle ? Can any one guide how to do this. The objects are uniformly distributed $\rho (x,y)$. Thanks, najma Thanks ...
0
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1answer
28 views

Find rectangles whose area increases by a factor of 20 when their length and width increases by k

Is there an easy way of knowing which rectangles have the same property? (length+k)(width+k) = 20(length*width)
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2answers
26 views

The height of two triangles

My textbook says the height of the following triangles ($BC$) is $37.5$ Because $$ \widehat{B_1}=\widehat{B_2}=30 \Rightarrow BD=50 \Rightarrow DC=25 \Rightarrow AC=75 $$ and since in right ...
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2answers
32 views

Volume of a region?

It is my intuition that the volume of the solid such that $0\leq x_1 \leq x_2 \ldots \leq x_n \leq T$ is $\frac{T^n}{n!}$. Can someone confirm/deny and/or supply proof? Thanks!
2
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2answers
28 views

How to translate a vector and then rotate by a point

I am trying to do this problem: Identify the combination formed by first translating by the vector $(2,0)$ and then rotating by $90$ degrees about $(0,0)$. but I'm a bit confused so, I ...
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1answer
19 views

Given the parallelogram solve for z [closed]

Solve for z by using the parallelogram below.
4
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2answers
60 views

Deriving the value of $\pi$ from a dart board

I saw this on a website and it was pretty interesting: The circle inscribed in the square has a radius of $1$ and the square has a side length of $2$. This means that the area of the circle is: ...
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1answer
32 views

integral curves of vector fields

If we have a vector field on a boundary less and compact 2-manifold, which is neither a gradient nor a harmonic, does that imply its integral curves are closed?
2
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1answer
48 views

3D Dodecahedron model: Construction question.

The image below is a 2D construction that, when cut-out and folded appropriately (hopefully it is intuitively clear how to cut and fold), forms a 3D dodecahedron. It works great: I've successfully ...
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1answer
26 views

What is steepness, what is flatness?

I have 3 graphs rather like $$y = \frac{1}{x}$$ and I am supposed to describe which one is steepest and which one is flattest. This is for an Econ class, so I'm not sure the terminology being used is ...
2
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1answer
29 views

Area of Spherical Polygon

It appears to me that after repeated applications of Girard's theorem on the area of spherical triangles that we can obtain the surface area of a spherical polygon with interior angles ...
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2answers
39 views

A relation between area and diameter of a triangle

Let $|T|$ and $h_T$ the area and the longest side of a triangle $T$, respectively. Is there a constant $C$ (independent of the triangle) such that $|T|\leq C h_T$ ?
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0answers
90 views

Cabri 3D - Rotating a triangle

I'm given the exercise, in Cabri 3D, to rotate the triangle T around the axis AB and lead it via the triangle To to the triangle T'. I tried to rotate the triangle T around a fixed point and then ...
0
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1answer
59 views

What is the probability that a random line meet both of the opposite side of a square? [closed]

If it is known that a random line meets a side of a given square, show that the probability that it also meets the opposite side is p = sqrt2— 1.
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2answers
201 views

Insert squares into square

Let $ABCD$ be a square, $AB=2a$ Is it possible to insert two disjoint squares, both of side $a$ into $ABCD$?
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0answers
15 views

Convex pyramid with same pyramid volume formula

Areas $ A_1,A_2 $ of parallel planes are of $n$ sided polygons spaced distance/ height $H$ apart. How should generators of a solid be defined so that solid volume can continue to be calculated by the ...
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votes
0answers
8 views

Definition of collinear line segments in a 2D plane.

Let AB and CD be two straight line segments in a 2D plane. Can I say that AB and CD are collinear line segments when they lie along the same (infinite) straight line?
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0answers
27 views

Area of circles on a wall

If you are painting a wall that is 10 ft by 12ft blue with gray polka dots on it, and the polka dots are spaced their diameter's distance away from each other at the shortest distance, how much paint ...
0
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1answer
38 views

a question about how to parametrize a surface in $R^3$

Given a surface $$x^4/a^4+y^4/b^4+z^4/c^4=1$$,how can I parametrize the surface using X(u,v). I tried to use $x=a\sqrt{cos(\theta)sin(\phi)}$,$y=b\sqrt{cos(\theta)sin(\phi)}$,and ...
0
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1answer
16 views

Formula for Points of a Projection

Given a projection from the point $(-1,1)$ that maps $y = 2x$ onto $ y = 2x + 3$. How do I find a formula for where the points of $y = 2x$ map on $ y = 2x + 3$? Any assistance would be appreciated.
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0answers
27 views

Can I generate a skewed ellipse tangent to two points?

I'm trying to write a python script to generate a trailing edge (TE) for an airfoil with no TE. Basically want to make a smooth round-off nose profile to the right, the closure line should come out ...
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0answers
20 views

Isomorphism of projective general linear group and the general linear group modulo its center

I want to prove that $PGL(n,q)\cong GL(n,q)/Z(GL(n,q))$. (This is actually the usual definition for PGL if we study the matter algebraically but geometrically, this only comes as a theorem, as I have ...
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2answers
35 views

Find line equation using another line's equation and the angle

So, I have the problem described exactly as in the figure below. I want to find the equation for the green line given the data described in the figure. I know that $$\tan(\text{angle of elevation for ...
5
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1answer
42 views

Fitting a circle

Given a figure like , how can I determine the radius of the circle with middlepoint H analytically? CDFE is a square with sides 6/5, with E and F being points on the circles with radii 2.
1
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1answer
37 views

Find the image of circular points by fitting conics

According to Single Axis Geometry by Fitting Conics by Jiang et al., one can compute the image of the circular points in a picture from conics which are the images of circles. Fit two conics to ...
3
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2answers
110 views

Proper axiomatization of Euclidean Geometry that Euclid would approve of

It is relatively common knowledge that Euclid's axiomatization is not sufficient to prove all the things that Euclid wants to, and that there are other axiomatizations out there that strengthen ...
0
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1answer
38 views

Flex a square into a circle, and prove…

Let points $A$, $B$, $C$, and $D$ be the vertices on a square. Let $\overline{CD}$'s midpoint be $E$. Flex the square into a circle (so they'll have equal perimeter/circumference), and translate the ...
2
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2answers
63 views

Proving a Simple Fact about Slopes of Lines

The following problem is a detail from a proof I wrote recently -- a detail that I left unproven, and would like to prove. Let there be three points $a$, $b$, and $c = \frac{a+b}{2}$, with $a<b$. ...
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2answers
37 views

Find the coordinates of center for the composition of two rotations

The combination of a clockwise rotation about $(0, 0)$ by $120◦$ followed by a clockwise rotation about $(4, 0)$ by $60◦$ is a rotation. Find the coordinates of its center and its angle of rotation. ...
8
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1answer
61 views

Parallelizing lines

Let $n \geq 1$ be an integer, and $L_1,\ldots,L_n$ be $n$ lines in $\mathbb{R}^3$ which are pairwise disjoint. Is it possible to move all $n$ lines continuously so that they never cross, and so as to ...
2
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0answers
14 views

A Particular Decomposition of the Simplex

Suppose I have a simplex $S_n$ with unit side-lengths. Fix a vertex $V$. Let $A_n$ be the convex polytope whose points are contained within the simplex, where the euclidean distance from each point ...
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2answers
220 views

To whom do we owe this construction of angles and trigonometry?

I've come across what is, to me, the most precise, beautiful and thorough definition of what we know of as the angle between two vectors. I say this because most literature either skims over things ...
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0answers
7 views

Help Solving Trilateration Location Determination Example

I was reading about Trilateration on page 238 of this link: Trilateration Paper I pulled my equations from this paper. I made up some values for centers of 3 circles and an imaginary 'receiver' ...
0
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1answer
24 views

Send 3 space minus a ring onto the circle

Here's a topology problem I'm having trouble solving. I'm sure it's something simple. Let $S \subset \mathbb{R}^3$ be $\{z=0; x^2 + y^2 =1\}$. Show that there is a continuous function from ...
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0answers
49 views

20th century books on geometry

I've heard something about the fact of some old geometry textbooks, dated to the beginning of the 20th century approximately, have a structure composed by a problem, the solution and then something ...
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1answer
20 views

Question in geometry on Fano Plane

Hello friends I have a geometry homework question asking me to do the following: I need to prove all projective planes of order two are isomorphic by showing they are all isomorphic to the Fano Plane. ...